In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compac...In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compact subset of real numbers. At the end of the paper the author applies this result for different classes of Q.展开更多
In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A ...In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Che...This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Chebyshev subspace of C （Q）, then for any admissible function f ∈ C（Q）／M, the best copositive approximation to f from M is unique.展开更多
In this paper,we discuss the relation between τ-strongly Chebyshev,approximatively τ-compact k-Chebyshev,approximatively τ-compact,τ-strongly proximinal and proximinal sets,where τ is the norm or the weak topolog...In this paper,we discuss the relation between τ-strongly Chebyshev,approximatively τ-compact k-Chebyshev,approximatively τ-compact,τ-strongly proximinal and proximinal sets,where τ is the norm or the weak topology.We give some equivalent conditions regarding the above proximinality.Furthermore,we also propose the necessary and sufficient conditions that a half-space is τ-strongly proximinal,approximatively τ-compact and τ-strongly Chebyshev.展开更多
In this paper, a new concept, strictly efficient points in locally convex spaces,is introduced, and scalar characterization of a strictly efficient point is established. Furthermore, we study the best approximation pr...In this paper, a new concept, strictly efficient points in locally convex spaces,is introduced, and scalar characterization of a strictly efficient point is established. Furthermore, we study the best approximation property for a strictly efficient point by an equivalent norm.展开更多
Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi...Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.展开更多
A spectral scheme is considered for solving the barotropic vorticity equation. The error estimates are proved strictly. The technique used in this paper is also useful for other nonlinear problems defined on a spheric...A spectral scheme is considered for solving the barotropic vorticity equation. The error estimates are proved strictly. The technique used in this paper is also useful for other nonlinear problems defined on a spherical surface.展开更多
文摘In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compact subset of real numbers. At the end of the paper the author applies this result for different classes of Q.
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
文摘This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Chebyshev subspace of C （Q）, then for any admissible function f ∈ C（Q）／M, the best copositive approximation to f from M is unique.
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)。
文摘In this paper,we discuss the relation between τ-strongly Chebyshev,approximatively τ-compact k-Chebyshev,approximatively τ-compact,τ-strongly proximinal and proximinal sets,where τ is the norm or the weak topology.We give some equivalent conditions regarding the above proximinality.Furthermore,we also propose the necessary and sufficient conditions that a half-space is τ-strongly proximinal,approximatively τ-compact and τ-strongly Chebyshev.
文摘In this paper, a new concept, strictly efficient points in locally convex spaces,is introduced, and scalar characterization of a strictly efficient point is established. Furthermore, we study the best approximation property for a strictly efficient point by an equivalent norm.
基金Supported by National Natural Science Foundation of China, Grant (10471032)
文摘Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.
文摘A spectral scheme is considered for solving the barotropic vorticity equation. The error estimates are proved strictly. The technique used in this paper is also useful for other nonlinear problems defined on a spherical surface.
